The Lagrangian Relaxation Method for Solving Integer Programming Problems

( This article originally appeared in Management Science, January 1981, Volume 27, Number 1, pp. 1–18, published by The Institute of Management Sciences. ) One of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy p...

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Bibliographic Details
Published in:Management science Vol. 50; no. Supplement 12; pp. 1861 - 1871
Main Author: Fisher, Marshall L
Format: Journal Article
Language:English
Published: INFORMS 01.12.2004
Institute for Operations Research and the Management Sciences
Series:Management Science
Subjects:
Algorithms
Business studies
Discrete mathematics
heuristic
Heuristics
Integer programming
Integers
Lagrangian function
Lagrangian functions
Management
Management science
Mathematics
Methodology
Optimal solutions
Problem solving
Programming
programming: integer algorithm branch and bound
programming: integer algorithms
programming: integer algorithms, heuristic
Scheduling
ISSN:0025-1909, 1526-5501
Online Access:Get full text
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Summary:( This article originally appeared in Management Science, January 1981, Volume 27, Number 1, pp. 1–18, published by The Institute of Management Sciences. ) One of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints. Dualizing the side constraints produces a Lagrangian problem that is easy to solve and whose optimal value is a lower bound (for minimization problems) on the optimal value of the original problem. The Lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm. This approach has led to dramatically improved algorithms for a number of important problems in the areas of routing, location, scheduling, assignment and set covering. This paper is a review of Lagrangian relaxation based on what has been learned in the last decade.
Bibliography:ObjectType-Article-2
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ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.1040.0263